Question 252470
Instead of radius I think you mean altitude of the triangle is 2sqrt(3).
If we use this assumption, your equilateral triangle is cut by this altitude into two 30-60-90 triangles.
The side opposite 60 degrees is 2sqrt(3). 
The side opposite the 30 degrees will be 2.
The hypotenuse (side of the equilateral triangle) will be 4. 
There are special formulas for the 30-60-90.
Now, we can find the area using the formula you stated in the question:
A = {{{s^2*sqrt(3) / 4}}}
A = {{{4^2*sqrt(3)/4}}}
A = {{{4*sqrt(3)}}}